5kyu-gapInPrimes.js

'use strict';

// Source: https://www.codewars.com/kata/561e9c843a2ef5a40c0000a4

// DESCRIPTION:

// The prime numbers are not regularly spaced. For example from 2 to 3 the gap is 
// 1. From 3 to 5 the gap is 2. From 7 to 11 it is 4. Between 2 and 50 we have the 
// following pairs of 2-gaps primes: 3-5, 5-7, 11-13, 17-19, 29-31, 41-43

// A prime gap of length n is a run of n-1 consecutive composite numbers between 
// two successive primes (see: http://mathworld.wolfram.com/PrimeGaps.html).

// We will write a function gap with parameters:

// g (integer >= 2) which indicates the gap we are looking for
// m (integer > 2) which gives the start of the search (m inclusive)
// n (integer >= m) which gives the end of the search (n inclusive)

// n won't go beyond 1100000.

// In the example above gap(2, 3, 50) will return [3, 5] which is the first pair 
// between 3 and 50 with a 2-gap.

// So this function should return the first pair of two prime numbers spaced with a 
// gap of g between the limits m, n if these numbers exist otherwise null.

// Examples:
// gap(2, 5, 7) --> [5, 7]
// gap(2, 5, 5) --> null
// gap(4, 130, 200) --> [163, 167]: [193, 197] is also such a 4-gap primes between 
// 130 and 200 but it's not the first pair)
// gap(6,100,110) --> null: between 100 and 110 we have 101, 103, 107, 109 but 101-
// 107 is not a 6-gap because there is 103 in between and 103-109 is not a 6-gap 
// because there is 107 in between.


function isPrime(n) {
    if (n === 2 || n === 3) return true;
    if (n % 2 === 0 || n % 3 === 0) return false;

    for (let i = 5; i ** 2 <= n; i += 6) {
        if (n % i === 0 || n % (i + 2) === 0) return false;
    }

    return true;
}

function gap(g, m, n) {
    if (g % 2) return null;
    if (m % 2 === 0) m++;
    if (n % 2 === 0) n--;

    let previousPrime = 0;

    for (let i = m; i <= n; i += 2) {
        if (isPrime(i)) {
            if (i - previousPrime === g) {
                return [previousPrime, i];
            } else previousPrime = i;
        }
    }

    return null;
}